Can someone solve this problem?

Question

The sum of the digits of a three-digit number is 12. If the hundreds digit is 3 times the tens digit and the tens digit is 1/2 the units digit, what is the tens digit of the number?

And, how do you solve it? What kind of equation would you use?

Answer 1

The number 100x + 10y + z (x,y,z are digits)

Equations:
x + y + z = 12
x = 3y
2y = z

solve for y.

d:

Answer 2

If abc is the three digit number we are given that

a + b + c = 12 and a = 3b and b = c/2 (which is same as c = 2b) we are required to find b.

Substituting a and c in the above, we can write

3b + b + 2b = 12

6b = 12

b = 12/6 = 2

So, the tens digit is 2. The units digit is 4 and the hundreds digit is 6. The number is 624

Answer 3

The tens digit is 2, the number is 624.
How does one solve it? Well i began testing with the ones digit of 2 (1 would not work obviously, nor would any odd numbers) and found that the sum would not be 12, so then i tried a units digit of 4, then the tens digit would have to be 2 and the hundred's would have to be 6, and the sum was 12, hence, we have found the answer.

A more mathematical approach has already been outlined above.

Answer 4

Let the 3 digit number be abc
a+b+c=12 (three digits add up to 12)
a = 3b (hundred digit 3 times the tens)
b = c/2 ( tens digit 1/2 the units digit)
Solve
3b+b+c=12
4b +c =12
4.c/2 +c =12
3c =12
c=4
b=2
a=3b=6
The number is 624

Answer 5

let x be the hundreds digit, y be the tens digit and z be the units digit.
Since the sum is 12,
x+y+z=12
The hundreds digit is 3 times the tens, so
x=3y
The tens digit is 1/2 the units digit, so
y=1/2z
we can put that as
z=2y
subtitute x and z into the first equation
x+y+z=12
3y+y+2y=12
6y=12
y=2
The tens digit number is 2.

Answer 6

well Namaste, let's assume that the number is xyz. i.e. x= the hundreds digit
y= tens digit
z= units digit
now the sum of the three digits is 12

so x+y+z=12 ------- #1

the hundreds digit is 3 times the tens digit

so x=3*y ----------- #2

the tens digit is 1/2 the units digit

so y=0.5*z
which means that z=2*y--------- #3

subsituting from #2 and #3 into #1 we have that

3*y+y+2*y=12
6*y=12
so y=2
substituting in # 2 and # 3
x=6 & z=4
i.e. the number is 624

Answer 7

let the three digit number be represented by xyz.

The sum of the digits is 12

x + y + z = 12

The hundreds digit is 3 times the tens digit

x = 3y

The tens digits is 1/2 the units digit.

2y = z

Now solve for y

Answer 8

let the digits be x,y,z so x+y+z=12 and x=3y and y=z/2
so 6y=12 so y=2 and x=6 and z=4 so the number is 624

Answer 9

Let the number be written: ABC.
We are looking to find B.
We know:
A = 3B
B = C/2 or C = 2B
A+B+C = 12

So substitute the first two into the third:
3B + B + 2B = 12
6B = 12
B = 2 is the ten's digit.

(and then A = 3B = 6; C = 2B = 4)

Answer 10

If the number is abc then you have three equations:
a+b+c=12; a=3b ; 2b=c
Substitute for a and c =>
3b+b+2b=12, therefore b=2, a=6 and c=4
The number is 624